ES2914042T3 - Method and apparatus for commissioning branch circuit voltage sensors and branch circuit current sensors for branch circuit monitoring systems - Google Patents

Abstract

A method for a branch current monitoring system (2) employing a bi-phase Wye wiring configuration, wherein the branch current monitoring system (2) has a first phase and a second phase, the method comprising: obtaining a voltage measurement using a voltage sensor (24) associated with the first phase; obtaining a current measurement using a branch circuit current sensor (34), wherein the branch circuit current sensor (34) is arranged to measure a phase current of the first phase; determine a phase angle between the voltage measurement and the current measurement; and using the phase angle and a set of rules including a plurality of predetermined rules to identify at least one phase association and at least one polarity for the branch circuit current sensor (34), wherein the use of the angle and the rule set comprises: determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a normal polarity or (ii) associated with the second phase with a normal polarity. inverted in response to the phase angle satisfying a first of the rules; or determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a reversed polarity or (ii) associated with the second phase with a normal polarity in response to the angle of phase satisfies a second of the rules, wherein the first of the rules comprises that the phase angle is within a first range or a second range and the second of the rules comprises that the phase angle is within a third range, and where the first range is greater than or equal to 0° and less than 20°, where the second range is greater than 320° and less than 360°, and where the third range is greater than 140° and less than 200° °; or determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a normal polarity or (ii) associated with the second phase with a reversed polarity in response to the angle of phase satisfies a third of the rules; or determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a reversed polarity or (ii) associated with the second phase with a normal polarity in response to the angle of phase satisfies a fourth of the rules, where the third of the rules comprises that the phase angle is within a fourth range and the fourth of the rules comprises that the phase angle is within a fifth range, and where the fourth range is greater than 20° and less than 80°, and wherein the fifth range is greater than 200° and less than 260°.

Description

DESCRIPTION

Method and apparatus for commissioning branch circuit voltage sensors and branch circuit current sensors for branch circuit monitoring systems

Background

Countryside

The concept described refers generally to power or energy meters in polyphase power systems and, more particularly, to the commissioning and diagnostics of voltage sensors and current sensors in different wiring configurations for circuit monitoring systems. branch cables used in polyphase power systems.

background information

In a branch circuit monitoring system, a service panel typically has bus bars that have polyphase voltages that can be measured using voltage sensors. In addition, the panel also has multiple main current sensors on the busbars. On the other hand, the service panel may have branches and associated branch circuit current sensors. For proper measurement, it is critical that those voltage and current sensors are configured correctly. Misconfigurations frequently involve voltage sensors wired to wrong phases, branch circuit current sensors associated with wrong phases, or incorrectly grouped branch circuit current sensors.

A conventional approach to commissioning and diagnosing a branch circuit monitoring system is based on an understanding of the physical design of the system and the values measured by the voltage and current sensors, values that are used to calculate actual power values. reactive and apparent. Branch circuit current sensors are grouped based on physical design, which are used to calculate branch power. A failure to understand the physical design of the system frequently results in incorrect configuration. Incorrect settings can produce real, reactive, apparent, and similar branch energy values.

Attention is focused on document US 2015 042 311 A1, which shows a system for a three-phase power supply system that includes a plurality of voltage sensors that detect three-phase voltages of the three-phase power supply system, a plurality of current sensors that sense three-phase currents of the three-phase power system, and a number of analog-to-digital transformers that convert the sensed three-phase voltages and sensed three-phase currents of the three-phase power system to corresponding digital values. A processor calculates from the corresponding digital values at least two phase angles between voltage and current for at least two of three phases of the three-phase power system, diagnoses polarities and phase associations for at least two of the current sensors based on in, for each of the at least two current sensors, a predetermined three-phase power system wiring configuration and a corresponding one of the at least two phase angles are within a corresponding predetermined angular range, and outputs diagnostic results corresponding.

Summary

According to the present invention, a method, a module and a readable medium as described in claims 1, 2 and 3 are provided. In one embodiment, a method according to claim 1 is provided for a power current monitoring system. branch employing a bi-phase Wye wiring configuration.

In another embodiment, a branch circuit meter module according to claim 2 is provided for a branch current monitoring system employing a bi-phase Wye wiring configuration. Figs. 1A and 1B are a schematic diagram of a branch circuit monitoring system according to an illustrative non-limiting embodiment in which the described concept can be implemented;

Fig. 2 is a circuit diagram of an illustrative 4-wire, 3-phase Wye wiring configuration; Fig. 3 is a circuit diagram of an illustrative 3-wire 3-phase Delta wiring configuration; Fig. 4 is a circuit diagram of an illustrative 4-wire, 3-phase Delta wiring configuration; Fig. 5 is a circuit diagram of an illustrative three-phase grounded Delta wiring configuration; Fig. 6 is a circuit diagram of an illustrative bi-phase Wye wiring configuration;

Fig. 7 is a circuit diagram of an illustrative single-phase 3-wire wiring configuration; Fig. 8 is a schematic diagram of an overall architecture of a method and apparatus for current sensor diagnosis according to an illustrative embodiment as implemented by/in the branch circuit monitoring system of Figs. 1A and 1B;

Fig. 9 is a phasor diagram Van, Vbn, Vcn and Vab, VBc, VCa in a three-phase power system with balanced three-phase voltages;

Fig. 10A is a phasor diagram showing the relationship between voltages, VAn, VBn, and current measurements, /a, Ib according to one embodiment of the described concept;

Fig. 10B is a phasor diagram showing the relationship between voltage measurements, Van, Vbn, Vcn, and current measurements, /a, Ib according to one embodiment of the described concept;

Fig. 11 is a phasor diagram of voltages VAn, VBn, and voltage measurements, V ^an , V ^bn , V ^cn according to one embodiment of the described concept;

Fig. 12 is a phasor diagram showing the relationship between voltage measurements, V ^an , V ^{b n} , and current measurements, / ^a , I ^b according to one embodiment of the described concept; Y

Fig. 13 is a phasor diagram showing the relationship between voltage measurements, Van, and current measurements, I ^a according to one embodiment of the described concept.

Description of the preferred embodiments

As used herein, the statement that two or more pieces are "coupled" together means that the pieces are attached to each other directly or through one or more intermediate pieces.

As used herein, the term "number" means one or an integer greater than one (ie, a plurality).

As used herein, the term "processor" shall refer to a programmable analog and/or digital device that can store, retrieve, and process data; a computer; a workstation; a personal computer; a digital signal processor; a microprocessor; a microcontroller; a microcomputer; a central processing unit; a controller; a central computer; a minicomputer; A server; a network processor; or any suitable processing device or apparatus.

The disclosed concept provides a method and apparatus that diagnoses current sensor polarities and phase associations in different wiring configurations for protective relays or power or energy meters in polyphase power systems. The method and apparatus monitors the phase angles between voltage and current waveforms, and diagnoses polarity and phase associations of current sensors in different wiring configurations using the monitored phase angles. Currents and voltages are measured via voltage and current sensors, respectively, and the measured voltages and currents are converted to respective discrete voltage and current samples via analog-to-digital transformers. A phase angle between the voltage and current is calculated for each phase, and the polarities and phase associations of the current sensors under different wiring configurations are diagnosed based on the phase angle. Diagnostic results are output to indicate the determined polarities and phase associations. Diagnostic results can be stored and can be used for troubleshooting or other diagnostic purposes

The described concept provides a method and apparatus for validating branch circuit current sensor diagnostics based on real and reactive power calculations. In yet another aspect, the disclosed concept provides a method and apparatus for detecting the wiring configuration of an electrical power system based on a particular voltage ratio that is determined for the electrical power system. The described concept provides a method and apparatus for diagnosing voltage exchange conditions in an electrical power system. The details of each of these concepts described according to various illustrative embodiments are described in detail herein.

Figs. 1A and 1B are a schematic diagram of a branch circuit monitoring system 2 according to an illustrative non-limiting embodiment where the described concept can be implemented. To facilitate illustration, the branch circuit monitoring system 2 is divided between the two separate figures (Figs.

1A and 1B), with Fig. 1A showing the “Mains” and “Voltages” wiring and Fig. 1B showing the branch circuit wiring configuration.

As seen in Figures 1A and 1B, the branch circuit monitoring system 2 includes a primary power source 4, such as, without limitation, a utility power source, which in the illustrated embodiment is a utility power source. three-phase AC. The main power source 4 provides phases A, B and C to a ^{main circuit breaker} 6 ^{through a bus bar} 8 ^{having conductors} 8 ^A, 8 ^{B and} 8 ^{C. The main circuit breaker} 6 ^is a conventional 3 pole circuit breaker to provide a circuit protection functionality to the ^{branch circuit monitoring system 2. The output of the main circuit breaker} 6 ^{is coupled to a bus bar} 10 having conductors 10A (carrying phase A), 10B (carrying phase B) and 10C (carrying phase C).

As seen in Figures 1A and 1B, the branch circuit monitoring system 2 further includes a meter ^base 12 ^{to provide power metering functionality for the} branch circuit ^monitoring system 2 . First and second branch circuit meter modules 14A and 14B are coupled to meter base 12 as shown. Each branch circuit meter module 14 is structured to provide the functionality described briefly above and in greater detail herein. Although in the illustrated embodiment the branch circuit monitoring system 2 includes first and second branch circuit meter modules 14A and 14B as just described (each associated with a particular group of branch circuits), It will be understood that this is illustrative only, and that the functionality of the two branch circuit meter modules 14 may be combined in a single branch circuit meter module 14. Furthermore, the branch circuit monitoring system 2 also includes more than 2 branch circuit meter modules 14, for example four, six or eight such modules.

In the illustrative embodiment, each branch circuit meter module 14A, 14B comprises a computing device having a control system including a processor 16A, 16B and memory 18A, 18B. Processor 16A, 16B may be, for example, and without limitation, a microprocessor (pP), microcontroller, or some other suitable processing device, which is interfaced with memory 18A, 18B. Memory 18A, 18B may be any one or more of a variety of internal and/or external storage media types such as, but not limited to, RAM, ROM, EPROM(s), EEPROM(s), FLASH, and the like. similar that provide a storage register, ie, a machine-readable medium, for data storage such as in the manner of an internal storage area of a computer, and may be volatile memory or non-volatile memory. Memory 18A, 18B has stored therein a number of routines that are executable by processor 16. One or more of the routines implement (via computer/processor executable instructions) at least one embodiment of the methods briefly discussed above. and in greater detail below for ^{commissioning and diagnosing voltage and current sensors that form a part of the} branch circuit ^monitoring system 2 under different wiring configurations.

As seen in Figures 1A and 1B, branch circuit monitoring system 2 also includes a number of loads 20, labeled 20A-20F, which are powered by power received from main power source 4. In particular, as seen in Fig. 1B, each load 20 is coupled to one or more of the ^conductors 10A ^{, 10B, 10C of the main busbar} 10 ^{through an associated circuit breaker} 22 ^{, which may be} a 1-pole circuit breaker (labeled 22-1), a 2-pole circuit breaker (labeled 22-2), or a 3-pole circuit breaker (labeled 22-3), as appropriate.

In Fig. 1A, the branch circuit monitoring system 2 also includes voltage sensors 24A, 24B, 24C for measuring the voltage of each phase on the main bus 10, and current sensors 26A, 26B, 26C for measuring the current of each phase in the main busbar 10. Each voltage sensor 24 may be, for example, and not limited to, a conventional potential transformer, and each current sensor 26 may be, for example, and not limited to, a conventional current transformer. The branch circuit monitoring system 2 also includes a neutral voltage sensor 28 and a neutral current sensor 30 for measuring the voltage and current on a neutral line 32. The signals generated by the voltage sensors 24, the current sensors 26 current, neutral voltage sensor 28 and neutral current sensor 30 are provided to each branch circuit meter module 14 for use as described herein.

In Fig. 1B, the branch circuit monitoring system 2 includes a number of branch circuit current sensors 34, wherein, as seen in Fig. 1B, each ^{branch circuit current sensor 34 is associated with: (i) a particular phase of main bus} 10 ^{, (ii) a particular pole of a particular one} of the breakers 22, and (iii) a particular load 20. Each branch circuit current sensor 34 may be, for example, and not limited to, a conventional current transformer. The signals generated by the current sensors 34 are provided to one of the branch circuit meter modules 14 for use as described herein. In the non-limiting illustrative embodiment, signals generated by branch circuit current sensors 34 located on the left side of Fig. 1B and associated with circuit breakers 22 on the left side of main bus 10 are provided to the module branch circuit meter 14A, and the signals generated by the branch current sensors 34 branch circuit located on the right hand side of Fig. 1B and associated with circuit breakers 22 on the right hand side of main bus 10 are provided to branch circuit meter module 14B.

In the branch circuit monitoring system 2, as just described, voltage and current sensors 24, 26, 28, 30 and 34 are operable to measure voltage and current waveforms, respectively. Voltage measurements are typically acquired by voltage sensors of one phase relative to a separate phase, or one phase relative to a voltage reference point (eg, neutral). Furthermore, there are two types of current sensors in the branch circuit monitoring system 2. The first type of current sensor is the main current sensors 26 which are mounted on the conductors 10A, 10B and 10C of the main bus bar 10 at an entry point to, for example, a service panel, and measure currents. added for each phase. The second type of current sensor is the branch circuit current sensors 34 . Branch circuit current sensors 34 are mounted on each branch circuit associated with a respective load 20, and measure individual branch circuit current.

In the illustrative embodiment, analog-to-digital transformers 42, 44 described elsewhere herein (FIG. 8) are used to convert voltage and current measurements into discrete voltage and current samples, respectively, at a frequency of faith sampling. The sampling rate fe is typically expressed in hertz (Hz) or samples per cycle. For example, given an electrical power system with a utility frequency of fe = 60 Hz, a sample rate of 512 samples per cycle is equivalent to a sample rate of 30,720 Hz.

The voltage and current measurements described above depend on wiring configurations. For a branch circuit monitoring system 2 used in a 3-phase power system, the wiring configuration is typically one of the following possible cases: Wye 3-phase 4-wire; 3-wire 3-phase delta; 3-phase 4-wire delta; 3-Phase Delta with Ground; Biphasic Wye; Single phase 3 wires; and Single-phase 2-wire. For each wiring configuration, the voltage and current sensors 24, 26, 28, 30 and 34 are configured accordingly to provide voltage and current measurements. Description of various wiring configurations

The description provided below outlines the voltage and current measurements that are associated with each particular wiring configuration listed above. That description will be helpful in understanding the particularities of the various aspects of the concept described elsewhere herein.

Wye 3-phase 4-wire

Fig. 2 is a circuit diagram 36A of an illustrative 4-wire, 3-phase Wye wiring configuration. In practice, the neutral N is connected to ground G through at least one resistor with high resistance to suppression of overvoltages caused by tripping arcs.

In the 3-phase 4-wire Wye wiring configuration, voltage measurements are typically obtained by voltage sensing one phase relative to a voltage reference point, or one phase relative to a separate phase. For example, when voltage measurements are acquired by single-phase voltage sensors relative to a voltage reference point in Fig. 2, a voltage sensor intended for voltage measurement V ^an is configured to measure phase voltage. phase A to neutral N. A second voltage sensor intended to measure voltage VB ⁿ is configured to measure phase B to neutral N voltage. A third voltage sensor intended to measure voltage V ^cn is configured to measure voltage from phase C to neutral N.

Alternatively, when voltage measurements are acquired by voltage sensors of one phase relative to a separate phase in Fig. 2, a voltage sensor intended for voltage measurement V ^ab is configured to measure phase voltage A to phase B. A second voltage sensor intended for voltage measurement VB ^c is configured to measure voltage from phase B to phase C. A third voltage sensor intended for voltage measurement V ^ac is configured to measure voltage from phase C to phase A.

It is worth noting that the voltage measurements V ^ab , VB ^c , V ^ca are related to the voltage measurements V ^an , V ^bn , V ^cn by:

^{Vab =Van -Vbn ( 1} )

^Vbc = ^{Vbn -Vcn} (2)

V ^ac =V ^cn -V ^an (3)

In Fig. 2, the positive direction of AI phase current measurement ^a is defined as node “A” to node “n”, and the voltage VAn is defined as the voltage at node “A” with respect to to the voltage at node “n” in the same figure. Likewise, similar definitions apply to the quantities I ^b , I ^c , and VBn, Ven of phases B and C.

3-wire 3-phase delta

Fig. 3 is a circuit diagram 36B showing an illustrative 3-wire 3-phase Delta wiring configuration. The voltage rise Vab is defined as the voltage at node “A” relative to the voltage at node “B”, and the current ¡ ^ab is defined as the current flowing from node “A” to node “B”. Similarly, similar definitions apply to voltages V ^bc , V ^ac and currents ¡B ^c , ¡ ^ac .

In the Figure, the positive direction of the phase A current measurement of Ia is defined as from the source to node “A”. Similarly, similar definitions apply to the quantities ¡B and ¡c of phases B and C.

3-phase 4-wire delta

Fig. 4 is a circuit diagram 36C showing an illustrative 3-phase 4-wire Delta wiring configuration. This is also known as a high leg delta wiring configuration. In practice, node “N” in a 3-phase 4-wire Delta system is usually accessible, while node “n” in the same 3-phase 4-wire Delta system is not always provided. Therefore, voltage measurements Van, Vbn, Vcn and current measurements ¡ ^a , ¡ ^b , ¡ ^c are available, while voltages VAn, VBn, Ven are typically not available.

3-Phase Delta with Ground

Fig. 5 is a circuit diagram 36D showing 36C an illustrative 3-phase Delta with ground wiring configuration. In practice, the “N” node in a grounded 3-phase Delta system is usually accessible, while the “n” node in the same grounded 3-phase Delta system is not always provided. Therefore, voltage measurements V ^an , V ^cn and current measurements ¡ ^a , ¡ ^c are available, while voltages VAn, VBn, Ven are typically not available.

Biphasic Wye

The 2-phase Wye wiring configuration is a special case of the 4-wire 3-phase Wye wiring configuration. In a biphasic Wye system, only 2 of 3 phases are used. For example, Figure 6 is a circuit diagram 36E showing an illustrative bi-phase Wye wiring configuration with only Z ^a and Z ^b connected to the load side. In practice, the neutral N is connected to ground G through at least one resistor with high resistance to suppression of overvoltages caused by tripping arcs.

Single phase 3 wires

Fig. 7 is a circuit diagram 36F showing an illustrative 3-wire single phase wiring configuration. This is also known as a split phase wiring configuration. Unlike 3-phase wiring configurations, nodes “A”, “B”, and “N” are all outputs from a plant tapped transformer, with neutral node “N” typically grounded.

According to Fig. 7, given the balanced transformer outputs, the voltage measurements V ^an and V ^bn have the following relationship:

Van=-Vbn. (4)

2-wire single phase

The 2-wire single-phase wiring configuration is a special case of the 3-wire single-phase wiring configuration. In a single phase 2 wire system, only 1 of 2 phases are used. For example, referring to 7, when only Za is connected, then the original 3-wire single-phase Wye system becomes a 2-wire single-phase system.

Branch Circuit Current Sensor Diagnostics

A particular aspect of the disclosed concept provides a branch circuit current sensor diagnostic methodology that determines if a branch circuit current sensor has been configured with correct polarity and associated with correct phase. The branch circuit current sensor diagnosis of the described concept, described in more detail below, first obtains wiring configuration information, and then uses the phase angle between the voltage and current to determine the current sensor configuration. .

In connection with the implementation of this aspect of the described concept, various methods are provided for calculating the phase angle between voltage and current. Diagnostic methods are also provided for determine if a branch circuit current sensor has been configured with correct polarity and is associated with a correct phase that is particular to each wiring configuration.

Fig. 8 shows an overall architecture of a current sensor diagnostic method and apparatus according to an illustrative embodiment as implemented by/in the branch circuit monitoring system 2 including branch circuit meter modules 14 . The method and apparatus include the following five parts or steps: (1) voltage and current measurements 38 and 40 are detected by voltage sensors 24, 28 and current sensors 26, 30, 34, respectively; (2) the voltage and current measurements 38 and 40 are converted to the respective voltage and current samples 46, 48 by analog-to-digital (ADC) transformers 42, 44; (3) a phase angle 50 between the voltage and current is typically calculated for phases A, B, and C; (4) current sensor polarities and phase association diagnostics 52 are determined based on predetermined wiring configurations 54 (see description provided elsewhere herein for a methodology for automatically determining wiring configurations 54 according to a further aspect of the described concept); and (5) diagnostic results 56 are output and may be stored and may be used for troubleshooting or other diagnostic purposes. A suitable processor 16 forming a part of each branch circuit meter module 14 as described herein is employed for the last three parts or steps 50, 52, 56. The processor 16 may be coupled to a display 58 example for the output of diagnostic results 56. Although two ADCs 42, 44 are shown, a single ADC having a plurality of channels may be used to output digital samples of the detected voltages and currents.

As just described, the branch circuit current sensor diagnostic methodology of the described concept determines if a branch circuit current sensor 34 has been configured with a correct polarity and is associated with a correct phase. In particular, the methodology first obtains wiring configuration information and then uses the phase angle between the voltage and current to determine the current sensor configuration. Described below are two alternative methods that can be used to calculate the phase angle between voltage and current to implement the described concept branch circuit current sensor diagnostic methodology.

In a first method, for each phase, such as phase A, B, or C shown in Figures 1A and 1B, the phase angle between the voltage and current can be calculated by counting the number of samples Nz from the time of zero crossing of the voltage sample at the time of zero crossing of the current sample. Because the sampling frequency fe is a known quantity, the number of samples from the zero crossing time of the voltage sample to the zero crossing time of the current sample can be converted to a quantity of time T ^z (in seconds) by:

Tz=Nz/ is. (5)

where fe is in hertz (Hz).

Since the utility frequency fe (in Hertz) of the three-phase electrical power system is typically a known quantity, the amount of time Tz is further converted to a phase angle between the voltage and current, typically expressed in degrees (°) by:

<p=rem(360-Tz-fe, 360) (6)

where rem(-, 360) denotes the remainder of a quantity after it is divided by 360.

The operation wraps the phase angle between voltage and current to a non-negative value between 0 and 360°, and simplifies post current sensor diagnostics.

Following the above definition, when the voltage and current waveforms are in phase with each other, then the zero crossing times of the voltage and current sample are identical. Consequently, the phase angle between voltage and current is 0°. Otherwise, the phase angle between the voltage and current is a positive value less than 360°.

In a second method, when the real power P (in watts), the apparent power S (in volt-amperes), and the lead/lag information for each phase are available, the phase angle between the voltage and current for each phase is calculated by first calculating an intermediate phase angle p' using Table 1 below.

Table 1. Method for calculating the phase angle

In Table 1, arcs(-) is an arcsine function whose range is between 0 and n inclusive, that is, 0<arcs(-)<n. For example, if P<0 and forward, then y=-arcs(P/S).

The phase angle between voltage and current is obtained after the intermediate phase angle y' by:

y=rem[(y+2n')-180/n 360]. (7)

In addition, as described in detail below, according to a further aspect of the described concept, each different wiring configuration described herein has an associated set of rules for determining whether a branch circuit current sensor in the wiring configuration has been configured with a correct polarity and associated with a correct phase using the phase angle determined for the sensor in question.

More specifically, for a branch circuit current sensor 34 intended to measure phase A current in a 3-phase 4-wire Wye wiring configuration, there are 6 possible scenarios for this particular branch circuit current sensor 34:

1) The branch circuit current sensor 34 is wired to the phase A current carrying conductor with normal polarity. Consequently, the current measurement from the branch circuit current sensor is I ^a .

2) The branch circuit current sensor 34 is wired to the phase A current carrying conductor with a reversed polarity. Therefore, the current measurement of the branch circuit current sensor is - I ^a .

3) The branch circuit current sensor 34 is wired to the B phase current carrying conductor with a normal polarity. Therefore, the current measurement from the branch circuit current sensor is I ^b .

4) The branch circuit current sensor 34 is wired to the current carrying conductor of phase B with a reversed polarity. Therefore, the current measurement of the branch circuit current sensor is -I ^b .

5) The branch circuit current sensor 34 is wired to the phase current carrying conductor C with a normal polarity. Therefore, the current measurement from the branch circuit current sensor is I ^c .

6) The branch circuit current sensor 34 is wired to the phase current carrying conductor C with a reversed polarity. Therefore, the current measurement of the branch circuit current sensor is - I ^c .

Similarly, a branch circuit current sensor 34 intended to measure phase B or C current also has 6 possible scenarios in each case. According to the concept described, and as described in more detail below, the branch circuit current sensor diagnostic methodology determines which stage a particular branch circuit current sensor 34 has by analyzing the phase angle between the voltage and current according to a set of rules (in the form of a look-up table in the illustrative embodiment) that is specific to the particular wiring configuration in question, where the rules relate the phase angle to a particular sensor association and polarity.

In connection with the concept described, it is assumed that all voltage sensors 24, 28 have been configured correctly in polarities and phase associations. For example, in the illustrative 3-phase 4-wire Wye wiring configuration above, one voltage sensor 24 intended for measuring K ^an voltage is correctly configured to measure phase A to neutral N voltage. to voltage measurement K ^bn is configured to correctly measure phase B to neutral N voltage. A third voltage sensor 24 intended for voltage measurement K ^cn is configured to measure phase C to neutral N voltage.

Also, because most modern three-phase electrical power systems are regulated, three-phase voltages are assumed to be balanced, that is, the voltage measurements K ^an , K ^bn , K ^cn , when expressed in phasors, have the same amplitude and are 120 degrees apart.

Therefore, according to equations (1)-(3), the voltage measurements K ^ab , K ^bc , K ^c , when expressed in phasors, all have the same amplitude, and are 120° apart from each other, as it is shown in the phasor diagram 60 of Fig. 9.

For the purpose of the described concept, a three-phase symmetrical load is assumed, that is:

Z ^a = Z ^b = Z ^c = Z, (8)

and the load impedance phase angle, p, is limited to between 10° leading (capacitive load) and 50° lagging (inductive load). If the load impedance phase angle, p, is expressed as a non-negative value between 0 and 360°, then the above limit translates to 0°<p<50° and 350°<p<360°.

The above load impedance phase angle range includes: 1) purely resistive loads, where the load impedance phase angle is p=0°; 2) a major portion of inductive loads, including induction motors, where the load impedance has a lagging phase angle, ie, 0°<p<50°; and 3) certain capacitive loads, where the load impedance has a leading phase angle, ie, 350°<p<360°.

While the above assumption limits the load impedance phase angle p to a range of 0°<p<50° and 350°<p<360°, other load impedance phase angle ranges may alternatively be used. For example, in a system dominated by inductive loads, the load impedance phase angle p can alternatively be assumed to vary from 20° lagging (inductive load) to 80° lagging (inductive load), i.e. 20° <p<80°.

As stated above, for each wiring configuration described herein, the branch circuit current sensor diagnostic has a different set of rules for determining sensor phase association and polarity based on the determined phase angle. . Thus, according to one aspect of the concept described, each particular wiring configuration described herein has an associated table (referred to as the "Current Sensor Diagnostic Table") that summarizes the set of rules applicable to the particular wiring configuration. . The current sensor diagnostic methodology according to the described concept determines the polarity and phase association of the current sensor by reading appropriate entries in the appropriate table. Current Sensor Diagnostic Tables that are applicable to 3-phase 4-wire Wye wiring configurations; 3-wire 3-phase delta; 3-phase 4-wire delta; and 3-Phase Grounded Delta are described in detail in United States Patent Application Publication Number 2015/0042311. As a result, the rationale behind those tables is not discussed in detail here. Instead, the Current Sensor Diagnostic Table for each of those wiring configurations is provided below (Tables 2-5) for ease of use. In addition, one aspect of the described concept is the provision of the Current Sensor Diagnostic Table for bi-phase Wye wiring configurations; single phase 3 wires; and single-phase 2-wire, each of which is described in detail below (Tables 6-8).

Table 2. Current Sensor Diagnostics for 3-Phase 4-Wire Wye Wiring Configuration

Table 3. Current Sensor Diagnostics for 3-Phase 3-Wire Delta Wiring Configuration

Table 4. Current Sensor Diagnostics for 3-Phase 4-Wire Delta Wiring Configuration

Table 5. Current Sensor Diagnostics for 3-Phase Grounded Delta Wiring Configuration

The discussion will now turn to the current sensor diagnostic table for Wye 2-Phase, 1-Phase 3-Wire, and 1-Phase 2-Wire wiring configurations.

For biphasic Wye, the load impedance phase angle is limited to between 10° leading and 50° lagging. Therefore, the phase angle between the voltage VAn and the current measurement Ia varies from 10° leading to 50° lagging. In the same way, the phase angle between the voltage VBn and the current measurement Ib varies from 10° leading to 50° lagging. This is demonstrated by the phasor diagram 62A of Fig. 10A. Because there is no load connected between phase C and node “n” in biphase Wye wiring configuration (figure), therefore Ic=0.

Kirchhoff's current law dictates that the sum of the current measurements at node “n” is 0, that is, Ia+Ib=0. (9)

According to Figure,

Ia=Vâ Za, Ib= VBn/ZB. (10)

Substituting equation (10) into equation (9) yields

VAN/ZA+ VBnAZB=0. (eleven)

Note that equation (11) can be further simplified using the symmetric loading assumption in equation (8).

VAn+VBn=0. (12)

The voltage measurement V ^ab is related to VAn and VBn by

GAV=VAn-VBn (13)

Adding equation (12) to equation (13) yields

VaB=2 VAn (14)

Therefore, VAn=VAB/2, and VBn=-VAB/2. The resulting voltage measurements V ^an , V ^bn , and V ^cn , when expressed in phasors, are shown in the phasor diagram 64 of Fig. 11.

Since I ^c =0, therefore, if the amplitude of I ^a is 0, that is, |/ ^a |=0, where |-| denotes the amplitude of a phasor quantity, then the current sensor 34 intended to measure phase A current must have been erroneously associated with the phase C current carrying conductor.

Combine Figs. 10A and 11 produces Fig. 10B. Fig. 10B is a phasor diagram 62B showing relationships between voltage measurements Van, Vbn, Vcn, and current measurements Ia, Ib. Shaded areas in Fig. 10B indicate angular ranges of current measurements relative to voltage measurements.

Table 6 summarizes the cases in Fig. 10B, and shows the current sensor diagnostics for the bi-phase Wye wiring configuration. Note that in Table 6, pa denotes the phase angle between the voltage measurement V ^an and the current measurement from a current sensor 34 intended to measure the phase current A, ^pb denotes the phase angle between the voltage measurement V ^bn and the current measurement from a current sensor 34 intended to measure the phase current B. Since I ^c =0, the phase angle between the voltage measurement V ^cn and the current measurement from a current sensor intended to measure phase C current, eg is not available. Table 6. Current Sensor Diagnostics for Biphasic Wye Wiring Configuration

In a bi-phase wiring configuration, if a first branch circuit current sensor 34 is provided to measure phase A current, and a second branch circuit current sensor 34 is provided to measure phase B current, then there is 8 possible scenarios for these particular branch circuit current sensors 34.

1) The first branch circuit current sensor 34 is wired to the phase A current carrying conductor with a normal polarity. The second branch circuit current sensor 34 is wired to the B phase current carrying conductor with normal polarity. Therefore, the current measurement from the first branch circuit current sensor is Ia, and the current measurement from the second branch circuit current sensor is Ib.

2) The first branch circuit current sensor 34 is wired to the phase A current carrying conductor with a reversed polarity. The second branch circuit current sensor 34 is wired to the B phase current carrying conductor with normal polarity. Therefore, the current measurement from the first branch circuit current sensor is -I ^a , and the current measurement from the second branch circuit current sensor is Ib.

3) The first branch circuit current sensor 34 is wired to the phase A current carrying conductor with a normal polarity. The second branch circuit current sensor 34 is wired to the B phase current carrying conductor with a reversed polarity. Therefore, the current measurement from the first branch circuit current sensor is Ia, and the current measurement from the second branch circuit current sensor is -I ^b .

4) The first branch circuit current sensor 34 is wired to the phase A current carrying conductor with a reversed polarity. The second branch circuit current sensor 34 is wired to the B phase current carrying conductor with a reversed polarity. Therefore, the current measurement from the first branch circuit current sensor is -Ia, and the current measurement from the second branch circuit current sensor is -I ^b .

5) The first branch circuit current sensor 34 is wired to the B phase current carrying conductor with a normal polarity. The second branch circuit current sensor 34 is wired to the phase A current carrying conductor with normal polarity. Therefore, the current measurement from the first branch circuit current sensor is I b , and the current measurement from the second branch circuit current sensor is I ^a .

6) The first branch circuit current sensor 34 is wired to the phase B current carrying conductor with a reversed polarity. The second branch circuit current sensor 34 is wired to the phase A current carrying conductor with normal polarity. Therefore, the current measurement from the first branch circuit current sensor is -I b, and the current measurement from the second branch circuit current sensor is Ia.

7) The first branch circuit current sensor 34 is wired to the B phase current carrying conductor with a normal polarity. The second branch circuit current sensor 34 is wired to the phase A current carrying conductor with a reversed polarity. Therefore, the current measurement from the first branch circuit current sensor is I b , and the current measurement from the second branch circuit current sensor is -I ^a .

8) The first branch circuit current sensor 34 is wired to the current carrying conductor of phase B with a reversed polarity. The second branch circuit current sensor 34 is wired to the phase A current carrying conductor with a reversed polarity. Therefore, the current measurement from the first branch circuit current sensor is -I ^b , and the current measurement from the second branch circuit current sensor is -I ^a .

According to Table 6, for the first branch current sensor 34, if 140'< ^pa < 200°, then the first branch current sensor 34 is not correctly wired to phase A current carrying conductor with normal polarity . Therefore, cases 2), 4), 5) and 7) in the above list can be detected as miswiring.

According to Table 6, for the second branch current sensor 34, if 200°<pb<260°, then this second branch current sensor 34 is not correctly wired to the phase B current carrying conductor with normal polarity . Therefore, cases 3), 4), 5) and 6) in the above list can be detected as miswiring.

According to Table 6, for the first branch current sensor 34, if 0°<pa<20° or 320°<^a<360°, and for the second branch current sensor 34, if 20°<^b <80°, then case 1) or case 8) in the above list may result in such detection results.

In this case, to differentiate whether case 1) or case 8) in the above list is true, other flags, such as a phase tag attached to the current sensor, and a phase tag attached to the current-carrying conductor , they can help the final determination.

This description below describes steps for diagnosing current sensors 34 for the 3-wire single-phase wiring configuration using the phase angles between the voltage measurements K ^an , K ^bn and the current measurements Ia, Ib respectively.

Based on the 3-wire, single-phase wiring configuration (Fig. 7), Kan, Kbn voltage measurements are related to KAn, KBn voltages by

K ^to N= KAn (15)

Kbn= KBn (16)

Therefore, according to equations (15) and (16), KAn=-KBn.

Fig. 12 is a phasor diagram 66 showing the relationships between voltage measurements Kan, Kbn, and current measurements I ^a , I ^b . Shaded areas in Fig. 12 indicate angular ranges of current measurements relative to voltage measurements.

Table 7 summarizes the cases in Fig. 12, and shows the current sensor diagnostics for the 3-wire, single-phase wiring configuration. Note that in Table 7, pA denotes the phase angle between the voltage measurement Kan and the current measurement from a current sensor 34 intended to measure phase A current, ^ ^b denotes the phase angle between the voltage measurement K ^bn and current measurement from a current sensor intended to measure phase B current.

Table 7. Current Sensor Diagnostics for Single-Phase 3-Wire Wiring Configuration

According to Table 7, pa or pe alone cannot solely determine that the current sensor 34 is correctly associated with the intended phase current carrying conductor, and that the current sensor 34 has normal polarity. For example, for a current sensor intended to measure phase A current, if 0°< ^pa <50° or 350°< ^pa <360°, the current sensor can be either of the following two possible situations: 1) Current sensor 34 is associated with an A-phase current carrying conductor, and has normal polarity.

2) The current sensor 34 is associated with the current carrying conductor of phase B, and at the same time has a reversed polarity.

In this case, other indicators, such as a phase tag attached to the current sensor, and a phase tag attached to the current-carrying conductor, can aid in the final determination.

The 2-wire single-phase wiring configuration is a special case of the 3-wire single-phase wiring configuration. Fig. 13 is a phasor diagram 68 showing the relationships between voltage measurements Kan, Kbn, and current measurements Ia, Ib. Shaded areas in Fig. 13 indicate angular ranges of current measurements relative to voltage measurements.

Table 8 summarizes the cases in Fig. 13, and shows the current sensor diagnostics for the 2-wire, single-phase wiring configuration. Note that in Table 8, pa denotes the phase angle between the voltage measurement K ^an and the current measurement from a current sensor 34 intended to measure phase A current.

Table 8. Current Sensor Diagnostics for Single-Phase 2-Wire Wiring Configuration

Branch Circuit Current Sensor Diagnostic Validation

In the branch circuit monitoring system 2, after the current sensor diagnosis is performed as described herein for each branch circuit, the final results of the branch circuit current sensor diagnosis can be validated. further if the main current sensors 26 have been installed and configured in the same branch circuit monitoring system 2 . The discussion below describes the steps to validate branch circuit current sensor diagnostic results using real power P and reactive power Q.

For each branch circuit current sensor 34, the actual power P (in watts) and the apparent power S (in volt-amps) are available. In addition, the power factor PF is also available. Given a nonzero PF, the reactive energy Q (in vars) is then calculated by

where |PF| is the absolute value of the power factor.

For the following 4 wiring configurations: Wye 3-Phase 4-Wire, Delta 3-Phase 3-Wire, Delta 3-Phase 4-Wire, Delta 3-Phase Grounded, once sensor diagnostics are complete As described herein, each branch circuit current sensor 34 is associated with a phase A current carrying conductor 10A, or a phase B current carrying conductor 10B, or alternatively a conductor 10C. phase current carrying conductor C. A total phase A real power PA.total is obtained by summing real power quantities for all branch circuit current sensors 34 that are associated with a phase current carrying conductor 10A A. Similarly, a total B-phase real power PB,total is obtained by summing real power quantities for all branch circuit current sensors 34 that are associated with B-phase current carrying conductor 10B, and obtains a total real phase C energy P^ total by summing real energy quantities for all branch circuit current sensors 34 that are associated with conductor 10C of phase current carrying C. In the same way, ÜA.total, OB.total, Qc,total are obtained for the branch circuit monitoring system 2.

For the branch circuit monitoring system 2 based on the above 4 wiring configurations, the total amounts of real and reactive power are also calculated from the voltage measurements made by the main voltage sensors 24 and the current measurements performed by the main current sensor 26. They are denoted as P t^otal, PB.total, Pc,total and Ocotal, OB.total, Qc.total.

Table 9 below shows a method that can be used to validate branch circuit current sensor diagnostic results for the following 4 wiring configurations, Wye 3-Phase 4-Wire, Delta 3-Phase 3-Wire, Delta 3-Phase 4-Wire , and three-phase Delta with ground connection, according to an illustrative embodiment of an aspect of the described concept. For example, if PB,total=PB,total and OB,total=Ocotal, then the branch circuit current sensor diagnostic results are validated as Acceptable for all current sensors 34 associated with branch current carrying conductors. phase B. As another example, if PC,total^ Pc,total or QC,total^ OC,total, then the branch circuit current sensor diagnostic results do not validate as Acceptable for all associated current sensors 34 with phase C current carrying conductors.

Table 9. Branch Circuit Current Sensor Diagnostic Validation Using 3-Phase Reactive Power and Real Power Quantities

Following the method described above, for the following two wiring configurations: 2-Phase Wye and 3-Wire Single-Phase, a total A-Phase real power PA,total and a total A-Phase reactive power GA,total are obtained by adding the quantities of real and reactive power for all branch circuit current sensors 34 that are associated with a phase A current carrying conductor 10A, and a total phase B real power PB,total and a phase B reactive power are obtained total QB, total by summing the amounts of real and reactive power for all branch circuit current sensors 34 that are associated with a phase B current carrying conductor 10B.

For the same branch circuit monitoring system 2 based on the above 2 wiring configurations, the total amounts of real and reactive power are also calculated from the voltage measurements made by the main voltage sensors 24 and the measurements of current made by the main current sensor 26. They are denoted as PA,total, P,B,total, and QVtotal, Ocotal.

Table 10 below shows a method that can be used to validate branch circuit current sensor diagnostic results for the following 2 wiring configurations, Wye 2-phase and 1-phase 3-wire, according to another illustrative embodiment of one aspect of the concept described.

Table 10. Branch Circuit Current Sensor Diagnostic Validation Using Reactive Power and Bi-Phase Real Power Quantities

For the single-phase 2-wire wiring configuration, a total phase A real power PA,total and a total phase A reactive power GA.total are obtained by summing the real and reactive power quantities for all current sensors 34 . branch circuit that are associated with a phase A current carrying conductor 10A. The total amounts of real and reactive power, denoted as PA.total and QVtotal, are also calculated from the voltage measurements made by the sensors 24 main voltage and current measurements made by the main current sensor 26 .

Table 11 shows the method that can be used to validate branch circuit current sensor diagnostic results for single-phase 2-wire wiring configurations based on a further aspect of the described concept.

Table 11. Branch Circuit Current Sensor Diagnostic Validation Using Single-Phase Reactive Power and Real Power Quantities

Determining the wiring configuration

Next, a description is provided of a methodology for determining the number of phases in a system, such as the branch circuit monitoring system 2, and then further determining the wiring configuration of the system according to yet another aspect of the described concept. This methodology is, in the illustrative embodiment, performed using only the RMS voltage measurements made by voltage sensors 24, 28 and it is assumed that the unused voltage terminals of the branch circuit meter modules 14A, 14B are tied to the neutral voltage node comprising the neutral conductor 32.

The methodology of this aspect of the described concept uses Line to Line and Line to Neutral voltage measurements to determine the wiring configuration without phase angle information. In particular, the voltage sensors 24, 28 will provide Line to Neutral voltage measurements for each of the conductors 10A, 10B, 10C of the main bus 10 (i.e., each phase) to the circuit meter modules 14 branching. From that information, the branch circuit meter modules 14 can determine Line-to-Line voltage measurements for each of the conductors 10A, 10B, 10C of the main bus 10 (ie, each phase). To distinguish between single phase and polyphase systems, the methodology first establishes the number of Line to Neutral non-zero voltage measurements that are made by the voltage sensors 24, 28. If there are only two non-zero measurements, it can be established that the system is a single-phase, 2-wire configuration. If there are three non-zero measurements, the system could be a 2-phase, 3-wire single-phase, or 3-phase Wye configuration.

Also, Vmin refers to the smallest Line-to-Line voltage measurement, and Vmax refers to the largest Line-to-Line voltage measurement. If Vmax is equal to Vmin, the methodology will establish that the system is a three-phase system. If Vmax is twice the value of Vmin, the methodology will establish that the system is a biphasic division. If Vmax is greater than Vmin by a factor of the square root of 3, the methodology will establish that the system is a biphasic Wye. A particular illustrative embodiment determines the phase mathematically by determining the ratio of Vmin:Vmax and using the following limits (limits determined as the midpoint between the two expected values):

VKm i - n T7-V _ Vratio

Vmax

if Vreiation >0.789 then the wiring configuration is a three-phase configuration

if Velation <0.539 then the wiring configuration is a single phase 3 wire configuration

Yes. 0.789 > Vratio > 0.539 then wiring configuration is biphasic Wye configuration

If, under the methodology, the system is determined to be a 3-phase system, the system may be further classified as a Delta Grounded, Delta 4-Wire, or Wye Balanced 4-Wire depending on Line-to-Line voltage measurements. Neutral. A 3-Phase 3-Wire Delta can be classified by the absence of a Line to Neutral voltage measurement. In this regard, Vmin refers to the phase with the smallest Line-to-Neutral voltage measurement, and Vmax refers to the phase with the largest Line-to-Neutral voltage measurement. The methodology then divides Vmin by Vmax. For grounded Delta, the min value should be zero or close to it. In the case of a 4-wire Delta, also known as a High Branch Delta or a Center Tap Delta, the Vratio value is expected to be close to 1/1.73 or one over the square root of 3. In the case of a 4-wire Wye configuration, the value of Vratio will be 1 if the system is perfectly balanced, but certainly not much less than 1. Therefore, a suitable method of distinguishing between the three configurations identified above is as follows:

^V km in

= V ratio

Vmax

0.732 0

0.366

two

if Velation < 0.366, then voltage setting is Delta with ground

if 0.366 < Velation < 0.732 then voltage setting is Delta 4-Wire

if Velation > 0.732 then voltage setting is Wye 4-wire

Diagnosis of voltage exchange conditions

An additional aspect of the described concept relates to diagnosing voltage exchange conditions. For balanced wiring configurations, the voltage phases are interchangeable and indistinguishable from each other. However, configurations that use a Neutral Voltage can be miswired by swapping the Neutral voltage with a Live voltage (called neutral swapping). Also, in configurations with unbalanced voltages, miswiring between phases (called phase swapping) can occur. Both miswire errors can be diagnosed.

The Neutral Exchange can be produced in Wye 3-phase 4-wire, Delta 3-phase 4-wire, and Single-phase 3-wire configurations. To diagnose Neutral Exchanges with any of the three-phase configurations, the Line-to-Line voltage measurements are sampled (ie, each phase is sampled). Vmin refers to the phase with the smallest Line-to-Line voltage measurement, and Vmax refers to the phase with the largest Line-to-Line voltage measurement. The methodology then divides Vmin by Vmax. The following tables 12 and 13 show the possible Vratio values of a 120V ^ln based system for correct wiring, and sharing of Neutral with any phase of a 4-wire Wye or 4-wire Delta:

Table 12 - Neutral exchange for 4-wire Wye configuration

Table 13 - Neutral Exchange for 4-Wire Delta Configuration

Therefore, a suitable method of detecting whether the neutral conductor measurement point 32 has been wired correctly is as follows:

if Vreiation > 0.732 then the Neutral has been wired correctly

if Velación— 0.732 then the Neutral has been wired incorrectly

To diagnose a neutral swapping condition with the single-phase 3-wire configuration, a tone sample is taken from the Line-to-Neutral voltages of each phase. VA refers to the first voltage and VB refers to the second voltage. If one is less than the other by 1/ ² , then the lower one is swapped with neutral. The following table 14 shows example values of a system based on 120V ^ln for the correct wiring, and the exchange of Neutral with any phase:

Table 14 - Neutral exchange for single-phase 3-wire configuration

A phase swap condition can be detected in the 3-Phase 4-Wire Delta Phase Unbalanced configuration with its high leg identification. According to another aspect of the described concept, a sample of the Line to Neutral voltages of each phase is taken. V ^a , V ^b , and Ve refer to the voltages of each phase. The high branch can then be identified by the voltage with the highest value. The following table 15 shows example values of a system based on 120V ^ln :

Table 15 - Phase exchange for single-phase 3-wire configuration

A mismatch in the expected high branch with respect to the identified high branch would be miswiring.

Branch Circuit Sensor Group

According to a further aspect of the described concept, as part of the commissioning process for the branch circuit monitoring system 2, the branch circuit sensors 34 are grouped into virtual meters. These are highly dependent on the physical design of the branch circuit monitoring system 2, and can be diagnosed with information about the physical design, and with data from the associated pair voltage and current sensors.

For a polyphase system, the physical layout of the branch circuits (each ^{branch circuit being associated with a single pole of a circuit breaker} 22 ^{) is typically in repeating phase order, or repeating reverse phase order} . By identifying the position of each branch circuit in the physical layout of the branch circuit monitoring system 2, phase errors can be found if the branches do not follow one of the prescribed orders.

^{Below in Table 16 are typical physical layouts for} 6 ^{branch 3-phase and 2-phase systems} . Triphasic or biphasic systems that do not use one of these designs would generate an error.

^{Table 16 - Typical Physical Designs for} 6 ^{Branch Three-Phase and Two-Phase Systems}

One, two, or three branch circuit current sensors 34 can be grouped together to create a virtual meter. A virtual meter typically monitors different phases of the same balanced load, such as an HVAC or 3-phase motor, and typically physically adjacent to each other. Therefore, a typical virtual meter may define its branch circuits for active loads according to the following criteria: (i) each branch circuit and associated branch circuit current sensor 34 in a virtual meter should be linked to a different phase no duplicate phases; (ii) all branch circuits and associated branch circuit current sensor 34 in a virtual meter should have the same or similar phase angle; (iii) all branch circuits and associated branch circuit current sensor 34 in a virtual meter should have the same or similar current; (iv) all branch circuits and associated branch circuit current sensor 34 in a virtual meter should be adjacent in physical layout

By analyzing each current, phase angle, and position in the physical layout of each branch circuit and associated branch circuit current sensor 34, virtual meters can be identified with a high degree of confidence.

According to the described concept, the analysis begins with the identification of the possible virtual meters for each branch circuit and the associated branch circuit current sensor 34 according to the physical design of the branch circuit monitoring system 2 . For example, Table 17 below shows a typical branch circuit on a 3-phase system that can be part of up to 3 possible 3-phase meters or 2 possible 2-phase meters, as illustrated below.

Table 17 - Possible Virtual Meters for a Typical Branch Circuit

Branches and associated branch circuit current sensor 34 located near the edge of the physical layout will have fewer possible meters than those located farther from the edge.

This method only identifies 3-phase meters on 3-phase 4-wire wye and 3-phase 3-wire delta systems, and 2-phase meters on single-phase 3-wire systems.

Next, for each possible virtual meter, its branch circuit phase angle variance is calculated using this variance equation:

where x is each of the branch circuit phase angles in the possible virtual meter, u is the average of the branch circuit phase angles in the possible virtual meter, and N is the number of branches and sensors 34 of associated branch circuit current in the possible virtual meter. The variance of the branch circuit current for each possible virtual meter is also calculated using the same equation, where x is each of the branch circuit currents in the possible virtual meter, u is the average of the branch circuit currents in the possible virtual meter. branch in the possible virtual meter, and N is the number of branches and associated branch circuit current sensors 34 in the possible virtual meter.

Then, for each branch circuit and associated branch circuit current sensor 34, a candidate virtual meter is determined by comparing all variances of all possible virtual meters that include it. If one of the virtual meters that includes the branch circuit has the lowest branch circuit phase angle variance and the lowest branch circuit current variance, it is determined to be a candidate virtual meter. Otherwise, there is no candidate virtual meter for that branch.

If there is a potential virtual meter where each of its branch circuits has determined the potential virtual meter to be its candidate virtual meter, then that potential virtual meter is identified as a virtual meter with high confidence.

To increase confidence, a filter can be placed on the variances so that if the variance between phase angles or currents is too high, no candidate meter is identified.

While specific embodiments of the disclosed concept have been described in detail, those skilled in the art will appreciate that various modifications and alternatives to these details could be developed in view of the general teachings of the description. Consequently, the particular arrangements described are intended to be illustrative only and not limiting in terms of the scope of the described concept, which should be given the full breadth of the attached claims.

Claims (3)

A method for a branch current monitoring system (2) employing a bi-phase Wye wiring configuration, wherein the branch current monitoring system (2) has a first phase and a second phase, the method comprising: obtaining a voltage measurement using a voltage sensor (24) associated with the first phase; obtaining a current measurement using a branch circuit current sensor (34), wherein the branch circuit current sensor (34) is arranged to measure a phase current of the first phase; determine a phase angle between the voltage measurement and the current measurement; and using the phase angle and a set of rules including a plurality of predetermined rules to identify at least one phase association and at least one polarity for the branch circuit current sensor (34), wherein the use of the angle of phase and the set of rules comprises: determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a normal polarity or (ii) associated with the second phase with a reversed polarity in response to the phase angle satisfy one of the rules first; either determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a reversed polarity or (ii) associated with the second phase with a normal polarity in response to the phase angle satisfies a second of the rules, wherein the first of the rules comprises that the phase angle is within a first range or a second range and the second of the rules comprises that the phase angle is within a third range, and where the first ^{range is greater than or equal to} 0 ^{° and less than} 20 ^{°, where the second range is greater than} 320° and less than 360°, and where the third range is greater than 140° and less than 200° ; or determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a normal polarity or (ii) associated with the second phase with a reversed polarity in response to the angle of phase satisfies a third of the rules; either determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a reversed polarity or (ii) associated with the second phase with a normal polarity in response to the phase angle satisfies a fourth of the rules, wherein the third of the rules comprises that the phase angle is within a fourth range and the fourth of the rules comprises that the phase angle is ^{within a fifth range, and wherein the fourth range is greater than} 20 ^{° and less than 80°, and wherein the fifth range is greater than} 200 ^{° and less than 260°.} A branch circuit meter module (14) for a branch current monitoring system (2) employing a bi-phase Wye wiring configuration, wherein the system Branch current monitoring (2) has a first phase and a second phase, the branch circuit meter module (14) comprising: a control system (16, 18), wherein the control system (16, 18) stores and is structured to execute a number of routines, the number of routines being structured to: receiving a voltage measurement from a voltage sensor (24) associated with the first phase; receiving a current measurement from a branch circuit current sensor (34), wherein the branch circuit current sensor (34) is arranged to measure a phase current of the first phase; determine a phase angle between the voltage measurement and the current measurement; and using the phase angle and a set of rules including a plurality of predetermined rules to identify at least one phase association and at least one polarity for the branch circuit current sensor (34), wherein the routines are structured to use the phase angle and a set of rules in: determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a normal polarity or (ii) associated with the second phase with a reversed polarity in response to the phase angle satisfying a first of the rules; either determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a reversed polarity or (ii) associated with the second phase with a normal polarity in response to the phase angle satisfies a second of the rules, where the first of the rules comprises that the angle of phase is within a first range or a second range and the second of the rules comprises that the phase angle is within a third range, where the first ^{range is greater than or equal to} 0 ^{° and less than} 20 ^{°, where the second range is greater than} 320° and less than 360°, and wherein the third range is greater than 140° and less than 200°; either determining that the branch circuit current sensor (34) is one of: (i) associated with the first phase with a normal polarity or (ii) associated with the second phase with a reversed polarity in response to the phase angle satisfy a third of the rules; either determining that the branch circuit current sensor (34) is one of: (i) ^{associated with the first phase with a reversed polarity or (ii) associated with the second} phase with a normal polarity in response to the phase angle satisfies a fourth of the rules, wherein the third of the rules comprises that the phase angle is within a fourth range and the fourth of the rules comprises that the phase angle is ^{within a fifth range, and wherein the fourth range is greater than} 20 ^{° and less than 80°, and} wherein the fifth range is greater than 200° and less than 260°. 3. A non-transient computer-readable medium (18) that stores one or more programs, including instructions, which when executed by a computer, cause the computer to perform the method of ^claim 1 ^.